Título: Inhomogeneous percolation with random one-dimensional reinforcements

Data: 06/11/2024                      Horário: 15:30h

Palestrante: Alan Bruno do Nascimento (IM-UFRJ)

Local: Laboratório de Sistemas Estocásticos (LSE), Sala I-044-B, Centro de Tecnologia - UFRJ.

Abstract: In this talk, we introduce the Bernoulli percolation model and consider inhomogeneous percolation on random environments on the graph GxZ, where G is an infinite quasi-transitive graph and Z is the set of integers. In 1994, Madras, Schinazi and Schonman showed that there is no percolation in Z^d  if the edges  are open with a probability of q<1 if they lie on a fixed deterministic axis and with a probability of p<p_c(Z^d) otherwise. Here, we consider a random region given by boxes with iid radii centered along the axis 0xZ of GxZ. We allow each edge to be open with a probability of q<1 if it is inside this region and with a probability of p<p_c(GxZ) otherwise. The goal of the talk is to show that occurrence or not of percolation in this inhomogeneous model depends on how sparse and how large are the boxes placed along the axis. We aim to give sufficient conditions on the moments of the radii as a function of the growth of the graph G for percolation not to occur.

This is a joint work with Rémy Sanchis and Daniel Ungaretti.

Mais informações: https://ppge.im.ufrj.br/